Quantum molecular dynamics code

Continue Computer simulations to discover and understand chemical properties Examples of a molecular dynamics simulation in a simple system: the deposition of a copper (Cu) atom on a cold copper crystal (Miller index (001) surface). Each circle represents the position of an atom. The kinetic energy of the atom approaching from above is re-distributed among the other atoms, so instead of rebounding, it remains because of the attractive forces between the atoms. Molecular dynamics simulations are often used to study biophysical systems. Here you can see a 100 ps simulation of water. (source?) A simplified description of the standard molecular dynamics simulation algorithm when a predictor-proofreader integrator is used. The forces can be derived from the classical interatomi potentials (mathematically described as F = − ∇ V ( r →) {\displaystyle F=-abla V({\vec {r}})} ) or quantum mechanics (mathematically F = F = F = → ). There are big differences between different integrators; some don't have exactly the same highest order of terms as the flowchart, many also use higher-order time derivatives, and some use both the current and previous time steps in variable-time step schemas. Molecular Dynamics (MD) is a computer simulation method for analyzing the physical movement of atoms and molecules. Atoms and molecules can interact for a set period of time, so they see the dynamic evolution of the system. In the most common variant, the trajectory of atoms and molecules is determined by numerically solving Newton's motion formulas in a system of interacting particles, where forces between particles and their potential energies are often calculated using interatomodal potentials or molecular mechanics force fields. The method is mainly used in chemical physics, materials science and biophysics. Since molecular systems typically have a large number of particles, it is impossible to determine the properties of such complex systems analytically; The MD simulation bypasses this problem using numerical methods. However, long MD simulations are mathematically poor conditions, generating cumulative errors in numeric integration that can be minimized by properly selecting algorithms and parameters, but cannot be completely removed. For systems that obey the ergodic hypothesis, the evolution of a molecular dynamic simulation can be used to determine the macroscopic thermodynamic properties of the system: the time averages of the ergodic system correspond to the averages of the microcanonic ensemble. MD is also referred to as statistical mechanics numbers and laplace's vision of Newtonian mechanics to predict the future by animing nature forces [1] and allowing insight into molecular movement on an atomic scale. History MD originally In the early 1950s, after previous successes with Monte Carlo simulations, which themselves date back to the eighteenth century, for example, in the buffon needle problem, but were promoted by Rosenbluth and Metropolis in the statistical mechanics of Los Alamos National Laboratory in today's Metropolis-Hastings algorithm. Interest in the time development of N-body systems dates much earlier in the fifteenth century, starting with Newton, and remains in the sixteenth century largely due to the focus on celestial mechanics and issues such as the stability of the solar system. Many of the numerical methods used today were developed during this period, which prevents the use of computers; For example, the most common integration algorithm used today, the Verlet integration algorithm, was used by Jean Baptiste Joseph Delambre as of 1791. Numerical calculations with these algorithms can be considered to be MD manually.. As of 1941, the integration of many-body motion formulas with analog computers was carried out. Some have undertaken labor-intensive work on modeling nuclear movements using physical models, such as macroscopic spheres. The goal was to arrange them by copying the structure of the liquid and using it to test its behavior. J.D. Bernal said in 1962: ... I took numerous rubber balls and stuck them together with rods of assorted different lengths ranging from 2.75 to 4 inches. I tried to do this in the first place, as loosely as possible, working in my own office, interrupted every five minutes or so, and I can't remember what I did before the interruption. [2] Following the discovery of microscopic particles and the development of computers, interest extended beyond the test field of gravity systems to the statistical properties of matter. Fermi proposed the use of MANIAC I in 1953, also at the Los Alamos National Laboratory, to decipher the time evolution of the multi-organ system's motion formulas for systems subject to multiple force laws; Today, this core work is known as the Fermi-Pasta-Ulam-Tsingou problem. The time evolution of the energy of the original work can be seen in the figure on the right. One of the earliest simulations of the N-body system was performed by Fermi et al. on MANIAC-I to understand the origin of irreversibility. Here you can see the energy and time of a 64-particle system. In 1957, Alder and Wainwright used an IBM 704 computer to simulate perfectly flexible collisions between hard spheres. [4] In 1960, perhaps the first realistic simulation of matter, Gibson and his mts simulated radiation damage from solid copper using a Born-Mayer type of repellent interaction along with a cohesive surface In 1964, Rahman[6] published simulations of liquid argon using lennard-jones potential; the calculation of system properties, such as the self-diffusion rate, compared well with experimental data. [6] Application areas and limitations Were first used in theoretical physics, the MD method soon became popular in materials science, and since the 1970s it has been common in biochemistry and biophysics. MD is often used to refine the three-dimensional structure of proteins and other macromolecules based on experimental limitations of X-ray crystal or NMR spectroscopy. In physics, MD is used to examine the dynamics of directly un observable atomic-level phenomena, such as thin-layer growth and ion-substal plantations, as well as the physical properties of nanotechnology devices that have not yet been created or that cannot yet be created. In biophysics and structural biology, the method is often used to study the movements of macromolecules, such as proteins and nucleic acids, which can be useful for interpreting the results of certain biophysical experiments and modeling interactions with other molecules, such as docking ligands. In principle, MD can be used for ab initio prediction of protein structure by simulation of folding the polypeptide chain into random coils. The results of MD simulations can be tested by comparison with experiments measuring molecular dynamics, of which NMR spectroscopy is a popular method. MD-derived structure predictions can be tested through community-wide experiments in the critical assessment of protein structure forecasting (CASP), although the method has historically had limited success in this area. Michael Levitt, who was awarded the Nobel Prize in part for applying MD to proteins, wrote in 1999 that CASP participants generally did not use the method to ... central disruption of molecular mechanics, namely that minimizing energy or its molecular dynamics usually leads to a model that is less similar to the experimental structure. [7] The improvement of computational resources, which allow for ever longer md trajectories and modern improvements in the quality of force field parameters, has resulted in some improvements in both the structure forecast and the refinement of the homological model, without having reached the practical utility point in these areas; identified force field parameters as a key area for further development. [8] [9] [10] MD simulations have been reported in pharmacopharma development and drug design. [11] For example, Pinto and its mts performed MD simulations of the Bcl-Xl complexes to calculate the average position of the critical amino acids involved in ligand binding. [12] On the other hand, Carlson and his mts to identify compounds that complement the receptor, while causing minimal disruption to the conformation and elasticity of the active area. Snapshots Snapshots for pharmacomo development, the protein was sedated at constant intervals during the simulation to identify the preserved binding regions (preserved in at least three of the eleven frames). Spyrakis and his mts. it relied on the workflow of MD simulations, fingerprints ligands and proteins (FLAP) and linear discriminating analysis to identify the best ligand-protein conformations associated with pharmacophore templates based on retrospective ROC analysis of the resulting pharmacophagus. In order to mitigate the structure-based drug discovery modeling, vis-a'-vis the need for many modeled compounds, Hatmal and Mtsai proposed a combination of MD simulation and ligand-receptor intermolecular connections analysis to detect critical intermolecular relationships (binding interactions) in the redundant ones of a single ligand protein complex. Critical relationships can then be converted to pharmacohor models that can be used for virtual filtering. [13] The limitations of the method are related to the parameter sets used and the underlying molecular mechanics force field. A run in an MD simulation optimizes the potential energy rather than the free energy of protein [indiscussed – discuss], meaning that all entropic contributions to thermodynamic stability of protein structure are neglected, including conformation entropy in the polypeptide chain (the main factor that destabilizes protein structure) and hydrophobic effects (the main driver of protein folding). [14] Another important factor is intramolecular hydrogen bindings,[15] which are not specifically included in modern force spaces, but are described as interactions of atomic point charges with Coulomb. It's a crude approach, because hydrogen bindings are partly quantum mechanical and chemical in nature. Furthermore, electrostatic interactions are usually calculated in the dielectric constant vacuum, although the surrounding aqueous solution is much higher dielectric constant. The use of macroscopic dielectric constants over short interatomi distances is questionable. Finally, van der Waals interactions with MD are usually described by Lennard-Jones as potentials based on the Fritz London theory, which can only be applied in a vacuum. However, all types of van der Waals forces are ultimately of electrostatic origin and therefore depend on dielectric properties of the environment. [16] Direct measurement of the attractiveness between different substances (like the Hamaker constant) shows that the interaction between hydrocarbons in water is about 10% as in vacuum. [16] The environmental dependence of van der Waals forces is neglected in standard simulations, but can be inserted by developing polarizable force fields. Design limitations The design of molecular dynamics simulation should take into account the available computing power. Size of simulation (n = number of particles), time step and total duration be selected in such a way that the calculation can be completed within a reasonable period of time. However, simulations should be long enough to be relevant to the time scales of the natural processes examined. To get statistically valid conclusions from the simulations, the duration simulated must be the same as the kinetics of the natural process. Otherwise, it's similar to drawing conclusions about how a man walks, if only looking at less than a step. Most scientific publications on protein and DNA dynamics[17][18] use data from simulations ranging from nanoseconds (10-9 s) to microseconds (10-6 s). Multiple days up to the CPU are required to obtain simulations. Parallel algorithms allow you to distribute the load between PROCESSORS; for example, the spatial or force decay algorithm. [19] In a classic MD simulation, the most CPU-intensive task is to evaluate the potential impact depending on the internal coordinates of the particles. Within this energy rating, the most expensive is one of the unferred or non-covalent parts. For Big O marking, common molecular dynamics simulations can be scaled according to O (n 2) (\displaystyle O(n^{2})} if all pair-wise electrostatic and van der Waals interactions are explicitly considered. This calculation cost can be reduced by using electrostatic methods such as Ewald summation of the particle net ( O ( n log ⁡ ( n ) {\displaystyle O(n\log(n)} ), particle particle particle net (P3M) or good spherical cutting methods ( O ( n ) {\displaystyle O(n)} ). [summons required] Another factor that affects the total CPU time required for simulation is the integration time step size. This is the time between the evaluation of potential. The time step must be small enough to avoid discretization errors (i.e. less than the period associated with the fastest vibration frequency in the system). Typical time steps for classic md are in order of 1 femtosek second (10-15 s). This value can be extended by using algorithms such as shake constraint algorithm, which records vibrations of the fastest atoms (e.g. hydrogens). Several timescale methods have been developed that allow for longer time between updates to slower long-range forces. [20] [21] [22] When simulating molecules in the solvent, a choice should be made between explicit and implicit solvents. Explicit solvent particles (such as tip3P, SPC/E and SPC-f water models) should be calculated expensively by the force field, while implicit solvents use an average field approach. The use of the explicit solvent is computationally expensive, requiring the inclusion of about 10 times more particles in the simulation. But granularity and viscosity of explicit solvent is essential to reproduce properties of the dissolved molecules. This is especially important for reproducing chemical kinetics. In all kinds of molecular dynamics in dynamics the size of the simulation box must be large enough to avoid boundary conditions. Boundary conditions are often treated by choosing fixed values at the edges (which can cause artifacts) or using period boundary conditions in which one side of the simulation turns back to the other side, imitating a bulk phase (which can also cause artifacts). Schematic representation of the system's potential energy surface sampling with molecular dynamics (in red) compared to Monte Carlo methods (in blue). Micro-canonical ensemble (NVE) In the micro-canonical ensemble, the system is isolated from changes in moths (N), volume (V) and energy (E). This corresponds to an adiabatic process with no heat exchanger. The micro-canonical molecular dynamics trajectory can be considered an exchange of potential and kinetic energy, preserving total energy. For a system of N-particles with X {\displaystyle X} coordinates and V (\displaystyle V}, the following pairs of first order differentials marked Newton : F ( X ) = − ∇ U ( X ) = M V ( t ) (t ) {\displaystyle F(X)=-abla U(X)=M{\dot {V}}}(t)} V ( t ) = X ( t ) = X ( t ) . {\displaystyle V(t)={\dot {X}}(t).} The power function of the system is based on the X {\displaystyle X} particle coordinates. It is referred to simply as a potential physics or a force field for chemistry. The first equation is derived from Newton's laws of movement; the F {\displaystyle F} force applied to each particle in the system can be calculated as a negative gradient of U ( X ) {\displaystyle U(X)}. For each step, each particle's X{\displaystyle X} position and V{\displaystyle V} speed can be integrated with a sympathetic integrator method, such as Verlet integration. The evolution of X {\displaystyle X} and V {\displaystyle V} over time is called trajectory. Taking into account initial positions (e.g. theoretical knowledge) and speeds (e.g. randomised Gauss), we can count all future (or past) positions and speeds. One common source of confusion is the meaning of temperature in MD. We often have experience with macroscopic temperatures, which contain a lot of particles. But temperature is a statistical quantity. If there are a large enough number of atoms, the statistical temperature can be estimated from the current temperature, which can be estimated by comparing the system's movement energy to nkBT/2, where n is the number of degrees of freedom of the system. The temperature-related phenomenon is due to the small number of atoms used in MD simulations. Consider, for example, simulating the growth of a copper film, starting with a substrate containing 500 atoms and 100 eV of deposition energy. In the real world, 100 eVs of the deposited atom pass quickly and number of atoms ( 10 10 {\displaystyle 10^{10}} or more) without a large temperature change. However, if there are only 500 atoms, the substrate evaporates almost immediately due to deposition. Something similar is happening in biophysical simulations. The temperature of the system in the NVE naturally rises when macromolecules, such as proteins, undergo exothermic conformation changes and binding. Canonical ensemble (NVT) The quantity (N), volume (V) and temperature (T) of the substance in the canonical ensemble are preserved. It is also called constant temperature molecular dynamics (CTMD). In NVT, the energy of endothermic and exothermic processes is replaced by a thermostat. Several thermostat algorithms are available to add and remove energy from the boundaries of the MD simulation in a more or less realistic way, approaching the canonical ensemble. Popular methods of temperature control include speed resizing, Nosé-Hoover thermostat, Nosé-Hoover chains, Berendsen thermostat, Andersen thermostat and Langevin dynamics. The Berendsen thermostat can introduce the flying ice cube effect, leading to physical translation and rotation of the simulated system. It is not trivial to obtain the cononical distribution of conformations and speeds using these algorithms. How it depends on the size of the system, thermostat choice, thermostat parameters, time step and integrator is the subject of many articles in the field. Isothermal-isothermal (NPT) combination The amount of substance (N), pressure (P) and temperature (T) are preserved in the isothermic-isozoar isobaric ensemble. In addition to the thermostat, barostat is also required. It is best suited to laboratory conditions when the flask is open to room temperature and pressure. In the simulation of biological membranes, isotropic pressure control is inadequate. In the case of lipid bilayers, pressure control is performed under a constant membrane area (NPAT) or constant surface tension gamma (NPγT). Generic ensembles The replica exchange method is a generic combination. It was originally created to cope with the slow dynamics of disordered spin systems. It's also called parallel tempering. The replica replacement MD (REMD) preparation [23] tries to overcome the problem of multiple minimies by replacing the temperature of uncooperative copies of the multi-temperature system. Options in MD simulations Main articles: Interatomic potential, Force field and force field implementations Simulation of molecular dynamics requires the definition of a possible function or a description of the expressions on the basis of which the particles in the simulation interact. In chemistry and biology it is usually referred to as the force field and material physics as an interatomi potential. Options can be defined at many levels of physical accuracy; those who the data used in chemistry are based on molecular mechanics and embody the treatment of classical mechanics of particle-to-particle interactions, which can reproduce structural and conformational changes but are generally unable to reproduce chemical reactions. Reducing from full quantum description to classical potential will involve two main approximations. The first is the Born-Oppenheimer approach, which states that the dynamics of electrons are so fast that they are considered to react immediately to the movement of the nuclei. As a result, they can be treated separately. The second treats the nuclei, which are much heavier than electrons, than point particles, which follow the classic Newtonian dynamics. In classical molecular dynamics, the effect of electrons is approximated as a possible energy surface, which usually represents the soil state. If finer detail is required, quantum mechanics-based options are used; some methods seek to create hybrid classical/quantum potentials, where most of the system is classically managed but a small region is treated as a quantum system, usually undergoing chemical transformation. Empirical potentials empirical options used in chemistry are often referred to as force fields, while materials used in physics are called interatomi potentials. Most fields of chemistry are empirical and are made up of a summary of glued forces related to chemical bonds, bonding angles and bonding dihedrals, as well as to van der Waals forces and electrostatic charge. Empirical potentials represent quantum mechanical effects to a limited extent through ad hoc functional approximations. These options include free parameters such as atomic charge, van der Waals parameters, which reflect the estimation of the atomic radius, as well as the length, angle and dihedrali of the equilibrium bond; these are given by fitting them to detailed electronic calculations (quantum chemistry simulations) or experimental physical properties such as flexible constants, grid parameters and spectroscopic measurements. Due to the non-local nature of the non-binding interactions, they contain at least weak interactions between all particles in the system. It is usually calculated as a bottleneck in the speed of MD simulations. In order to reduce the cost of calculation, force fields use numerical approaches, such as shifted cutting radius, reaction field algorithms, particle mesh Ewald summary or new particle particle net (P3M). Chemical force fields usually use preset bonding agreements (except for ab initio dynamics) and are thus unable to explicitly model the process of chemical bonds and reactions. On the other hand, many of the options used in physics, such as bond order formalism can be several different coordinations between the system and bond bond Examples include brenner's hydrocarbon potential[26] and further improvements to the C-Si-H[27] and C-O-H[28] systems. The ReaxFF potential[29] is considered to be a fully reactive hybrid between binding mandate potentials and chemical force fields. Couple potentials versus many-body potentials the potential functions representing unferred energy are formulated as an amount of interactions between the particles of the system. The easiest choice, applied to many popular force fields, is the pair of potentials in which the total potential energy can be calculated by the amount of energy contributions between pairs of atoms. Therefore, these fields of force are also called additive force fields. An example of such a pair of potentials is the unferred Lennard-Jones potential (also known as the 6-12 potential), used to calculate van der Waals forces. U ( r ) = 4 ε [ ( σ r ) 12 − − ( σ r ) 6 ] {\displaystyle U(r)=4\varepsilon \left[\'left({\frac {\sigma }{r}}\right)^{12} left-*left({frac {\sigma }{r}}\right)^{6}\right]} Another example is the Born (ionic) model of ionic lattice ice. The first term in the following equation is Coulomb's law of a pair of ions, the second term for short-term repulsion is explained by Pauli's exclusion principle, and the final term is the dispersion interaction term. In general, the simulation contains only the term dipolar, although sometimes the quadrupolar expression is included. [30] [31] When nl=6, this potential is also called the Coulomb-Buckingham potential. U i j ( r i j ) = z i z j 4 π ε 0 1 r i j + A l exp ⁡ − r i j p l + C l r i j − n l + { {\displaystyle U_{ij r_})={{\frac {z_{i}z_{j}}{4\pi \\epsilon _{0}}}{\frac {1}{r_{ij}}}+A_{l}\exp {\frac {-r_{ij}}}{p_{l}}}r_{l}C_ r_{ij}^{-n_{l}}+\cdots } , potential energy includes the effects of three or more particles interacting with each other. [32] Simulations with the potential of the pair also have global interactions in the system, but only in pairs. In the many-body potential, potential energy is not found by the amount above the atomic pairs, as these interactions are specifically calculated as a combination of higher expressions. In statistical view, dependency between variables cannot usually be expressed only by the pair of freedoms. For example, the Tersoff potential,[33] which was originally used to simulate coal, silicon, and Germanium and has since been used for many other materials, includes sums for three atomic groups, and atom-to-atom angles play an important role in potential. Other examples include the embedded atomic method (EAM),[34] the potentials of EDIP,[32] and the closely bound Second Moment Approach (TBSMA) potential,[35] where the electron density of states in the atom region is from the surrounding atoms, and the potential energy contribution is a function of this amount. Semi-empirical potentials Semi-empirical options use matrix depiction of quantum mechanics. However, the values of the matrix elements are found through empirical formulas that estimate the degree of overlap of each atomic circulation. The matrix then diagonally determines the utilization of different atomic orbits, and empirical formulas are once again used to determine the energy contributions of orbital orbits. There are a wide variety of semi-empirical options, called narrow bonding options, according to which changing the atoms modeling. Polarizable potentials Main article: Force field Most classical force areas implicitly involve the effect of polarization, for example by scaling up partial charges from quantum chemistry calculations. These partial charges are immobile compared to the mass of the atom. But molecular dynamics simulations can explicitly model polarity by introducing indued dipoles using different methods, such as Drude particles or fluctuating charges. This allows for dynamic redistribution of charge between atoms, which responds to the local chemical environment. For many years, polarized MD simulations have been touted as the next generation. Homogeneous liquids like water have achieved greater accuracy by recording polarization. [36] [37] [38] Some promising results have also been achieved for proteins. [39] However, it is still uncertain how best to approach polarization in a simulation. [summons required] Options ab initio methods Main articles: Quantum chemistry and list of quantum chemistry and solid state physics software for classical molecular dynamics, a potential energy surface (usually the soil state) is represented in the force field. This is a consequence of the Born-Oppenheimer approach. In agitated states, chemical reactions, or if more accurate representation is required, electronic behavior can be obtained from the first principles by a quantum mechanical method, such as density functional theory. This is Ab Initio Molecular Dynamics (AIMD). Due to the cost of managing electronic freedom levels, the cost of calculating these simulations is much higher than classical molecular dynamics. This means that AIMD is limited to smaller systems and shorter times. Ab initio quantum mechanics and chemical methods can be used to calculate the potential energy of a system on the fly, as needed for conformations on the trajectory. This calculation is usually performed in the vicinity of the reaction coordinate. Although different approximations can be used, they are based on theoretical considerations and not on empirical joins. Ab initio's calculations provide a huge amount of information empirical methods, such as the density of electronic states or other electronic properties. A significant advantage of the use of ab initio methods is the ability to study reactions that involve breaking or developing covalent bonds, which correspond to several electronic states. Furthermore, ab initio methods also allow you to recover effects beyond born- oppenheimer approaches using approaches like mixed quantum-classical dynamics. Hybrid QM/MM Main Article: QM/MM QM (quantum mechanics) methods are very powerful. However, they are computationally expensive, while MM (classical or molecular mechanics) methods are fast, but suffer from a number of limits (require extensive parameterization; the energy estimates obtained are not very accurate; they cannot be used to simulate reactions where covailing bonds are broken/formed; and limited in their capabilities to provide accurate details about the chemical environment). A new class of methods has been developed that combines the good points of qm (accuracy) and mm (speed) calculations. These methods are called mixed or hybrid quantum mechanical and molecular mechanical methods (hybrid QM/MM). [41] The most important advantage of the hybrid QM/MM method is speed. The cost of applying classical molecular dynamics (MM) in the simplest case scales O(n2), where n is the number of atoms in the system. This is primarily an expression of electrostatic interactions (each particle interacts with any other particle). However, the use of cut-off radius, periodic pair list updates and more recently variants of the particle mesh Ewald method (PME) has reduced this to o(n) o(n2). In other words, simulating a system containing twice as many atoms would require two to four times as much computing power. On the other hand, the simplest ab initio calculations are typically o(n3) or worse (limited Hartree-Fock calculations are suggested to scale ~O(n2.7). To overcome the limit, a small part of the system is treated quantum mechanically (typically at the active site of an enzyme) and the remaining system is classically treated. In more sophisticated implementations, QM/MM methods are used to manage both quantum-sensitive light cores (e.g. hydrogen) and electronic states. This allows for hydrogen wave functions (similar to electronic wave functions). This method was useful in investigating phenomena such as the hydrogen tunnel. One example where QM/MM methods have made new discoveries is the calculation of hydride transmission in the liver alcohol dehydrogenase enzyme. In this case, the quantum tunnel is important for hydrogen, as it determines the reaction rate. [42] Rough grainy and reduced representations On the other end of the detail scale, rough grainy and truss models Instead of specifically representing all the atoms of the system, it would represent, It uses pseudo-atoms to represent atomic groups. MD simulations on very large systems can require such large computer resources that they cannot be easily studied using traditional all-atom methods. Similarly, simulations of processes over a long period of time (about 1 microsecond) are prohibitively expensive because they require so many time steps. In these cases, sometimes it is possible to solve the problem by applying reduced depictions, also called rough-grained models. [43] Examples of rough grain (CG) methods are CG-DMD[44][45] and Go models. [46] Coarse graining is sometimes done by taking larger pseudoatoms. Such a united atom proximity was used in MD simulations of biological membranes. Applying such an approach on systems where electrical properties are interesting can be challenging due to the difficult way pseudoatoms are properly charged. [47] Lipids have an aliphatic tail represented by a few pseudoatoms, collecting 2-4 groups of methylene for each pseudoatom. The parameterization of these very coarse granular models shall be performed empirically by comparing the behaviour of the model with appropriate experimental data or all-atom simulations. Ideally, these parameters should implicitly take into account both enthalpic and entropic contributions to free energy. If coarse graining occurs at higher levels, the accuracy of the dynamic description may be less reliable. But very rough grainy models have been successfully used to examine a wide variety of issues in structural biology, liquid crystal icing, and polymer glasses. Examples of coarse granular applications: protein folding and protein structure prediction tests are often carried out using one or a few pseudoatoms per aminini; [43] liquid crystal phase transitions have been tested in closed geometries and/or during flow using the Gay-Berne potential, which denotes anisotropic species; Polymer glasses were tested during deformation using simple harmonic or FENE springs to connect the spheres described by the Lennard-Jones potential; DNA supercoiling has been studied using 1-3 pseudo-atoms in a basepair, and even lower resolution; The packaging of double-helix DNA into bacteriophages has been studied with models where a pseudoatom represents a turn of the double helix (about 10 basepairs); RNA structure of the ribosome and other large systems modeled on a pseudo-atom is a nucleotide. Virtual cell simulation to study the interaction between cells and various substrates. [48] The simplest form of coarse grains is the united atom (also known as an extended atom), which was used in early MD simulations of proteins, lipids, and nucleic acids. Such as that all four atoms of a CH3 methyl group would be specifically treated (or all three of CH2's atoms group), one representing the whole group with a pseudoatom. Of course, it should be properly parametered so that the interactions of van der Waals with other groups can have an appropriate distance dependence. Similar considerations apply to the joints, angles and torsions in which the pseudonym participates. In this type of uniform atom representation, one usually eliminates all explicit hydrogen atoms, except those that are able to participate in hydrogen bonds (polar hydrogen). An example is charmm 19. Polar hydrogens are generally retained in the model, as proper handling of hydrogen bindings requires a reasonably accurate description of the direction between donor and accepting groups and electrostatic interactions. For example, the hydroxyl group can be hydrogen bond donor and hydrogen bond acceptance, and this would be impossible to deal with with an OH pseudoatom. About half of the atoms are a protein or nucleic acid non-polar hydrogens, so the use of merged atoms can provide significant savings in computer time. Incorporation of solvent effects In many simulations of the soluble solvent system, the main focus is on the behaviour of the dissolved substance, in particular the representation of solvent behaviour, especially in solvent molecules living in regions far from the soluble molecule. [49] Solvents may affect the dynamic behaviour of the dissolved substance by random collisions and by dragging the movement of the dissolved substance through the solvent. The use of non-rectangular periodic boundary conditions, stocsastic boundaries and solvent shells can all contribute to reducing the number of solvent molecules needed and allowing a higher proportion of the calculation time to be spent simulating the dissolved material. The effects of the solvent can also be incorporated without the need for explicit solvent molecules. One example of this approach is the use of a potential mean force (PMF) that describes how free energy changes as a specific coordinate. The free energy change described by PMF contains the mean effects of the solvent. Long-range forces Long- range interaction is an interaction in which spatial interaction does not fall off faster than r − d {\displaystyle r^{-d}} where d {\displaystyle d} is the system dimension. Examples include charging interactions between ic ones and dipole dipole between molecules. Modeling these forces is quite challenging, as they are significant at a distance that can be greater than half the length of the box, with simulations of thousands of particles. While one solution would be to significantly increase the size of the box length, this brute force approach is less than ideal as the simulation would become computationally very expensive. Spherical truncation of potential is also out of the question, as behavior is observed when the distance is close to the cut-off distance. [50] Guided Molecular Dynamics (SMD) guided molecular dynamics (SMD) simulations or probe simulations use forces on a protein to manipulate its structure by dragging the desired levels of freedom. These experiments can be used to detect structural changes in protein at atomic level. SMD is often used to simulate events such as mechanical unfolding or stretching. [51] The SMD has two typical protocols: one in which the drag speed is constant and the force used in the other is constant. Typically, part of the test system (e.g. an atom in a protein) is limited by harmonic potential. Then the forces must be applied at constant speed or constant force to certain atoms. Umbrella sampling allows the system to move along the desired reaction coordinates, such as forces, distances, and angles manipulated in the simulation. With umbrella sampling, all configurations of the system, both high-energy and low-energy, are properly sampled. Then any configuration change in free energy can be calculated as a potential average force. [52] The popular method of calculating PMF is the Weighted Histogram Analysis Method (WHAM), which analyzes a series of umbrella sampling simulations. [53] Many important applications of SMD are in the fields of drug research and biomolecular sciences. For example, SMD was used to study the stability of protofibrills in Alzheimer's disease,[55] to study the interaction of the protein ligand in cyclin-dependent kinase 5[56] and even to show the effect of the electric field on the trombin (protein) and atamerre (nucleotide) complex[57] among many other interesting studies. Examples of applications molecular dynamics simulation of a synthetic molecular motor consisting of three molecules per nanopore (external diameter of 6.7 nm) to 250 K. Molecular dynamics are used in many disciplines. In 1975, the first MD simulation of the simplified biological folding process was published. His simulation, published in Nature, paved the way for a vast area of modern computer protein folding. [58] In 1976, the first MD simulation of the biological process was released. His simulation, published in Nature, paved the way for understanding protein movement as an essential feature and not just an accessory. [59] MD is the standard method for treating collision cascades in the thermal peak system, i.e. the effects of energetic neutron and ion irradiation on solid and solid surfaces. [60] The following biophysical examples show a remarkable effort to simulate systems of very large (full virus) or very long simulation time (up to 1.112 milliseconds): This virus: NAMD) This virus a small, icosaedral plant virus that exacerbates the symptoms of Tobacco Mosaic Virus (TMV) infection. Molecular dynamics simulations were used to test the mechanisms of viral assembly. The entire STMV particle consists of 60 identical copies of a protein that is made up of the virus capid (coating), and a 1,063 nucleotide single-stranded RNA genome. One of the most important findings is that kapidi is very unstable when there is no RNA inside. The simulation would be a 2006 desktop computer about 35 years to complete. Thus happened many processors in parallel with continuous communication between them. [61] Folding simulations of the Villin head in all atomic fragments (2006, Size: 20,000 atoms; Simulation time: 500 μs = 500,000 ns, Program: Folding@home) This simulation ran 200,000 CPU on participating personal computers from around the world. These computers have been the Folding@home program installed, a large-scale distributed computing effort coordinated by Vijay Pande at Stanford University. The kinetic properties of the Villin headdress protein were tested with a number of independent short trajectory that cpUs ran without continuous real-time communication. One method used was Pfold value analysis, which measures the probability of folding before expanding a specific initial conformation. Pfold provides information about the folding path along the transition state structures and sequence conformations. [62] Antonon performed long, continuous trajectory simulations on a massively parallel supercomputer designed and built around individual application-specific integrated circuits (ASICs) and connectors from D.E. Shaw Research. The longest published result of the anton simulation is the 1,112 millisecond simulation of NTL9 at 355 K; a second independent simulation of this configuration of 1.073 milliseconds was performed (and many other simulations with a continuous chemical time of more than 250 μs). [63] In How Fast-Folding Proteins Fold, researchers Kresten Lindorff-Larsen, Stefano Piana, Ron O. Dror, and David E. Shaw discuss the results of atomic molecular dynamics simulations in periods between 100 μs and 1 ms, which reveal common principles underlying the folding of 12 structurally different proteins. The examination of these varied long tracks, which are made possible by special, unique hardware, allows them to conclude that in most cases the folding follows a single dominant path, in which elements of the native structure appear in an order closely related to their willingness to form in an unfolded state. [63] In a separate study, Anton was replaced by a 1.013 millisecond simulation native dynamics of bovine pancreatic trypsin inhibitor (BPTI) at 300 K. [64] Molecular dynamics dynamics Filtered Coulomb Potentials Implicit Solvent Model Integrators Symplectic Integrator Verlet-Stoermer Integration Runge-Kutta Integration Beeman Algorithm Forced Algorithms (For Limited Systems) Short-Range Interaction Algorithms Cell Lists Verlet List Bonded Interactions Long-Term Interaction Algorithms Ewald Summary Particle Mesh Ewald Summary (PME) Particle -particle-particle-net (P3M) Shifted force method Parallelization strategies Domain decomposition method (Distribution of system data parallel computing) Ab-initio molecular dynamics Car-Parrinello molecular dynamics Special hardware MD simulations Anton - A special, massively parallel supercomputer designed, to perform MD simulations MDGRAPE - A special purpose system built for dynamics molecular simulations, especially protein structure prediction Graphics card as a hardware MD simulations Molecular modeling GPU See also molecular modeling computer chemistry force space (chemistry) Comparison of force field implementations Monte Carlo method Molecular design software Molecular mechanics Multiscale Green function Car-Parrinello method Comparison software molecular mechanics modeling Quantum chemistry discrete element method comparison nucleic acid simulation software Molecular editor Mixed quantum classic dynamics references ^ Schlick , Tamar (1996). 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